A glass density prediction method and system based on dimension constraint symbolic regression

Abstract

The application discloses a kind of glass density prediction methods based on dimension constraint symbol regression.The method utilizes dimension constraint symbol regression to filter key parameters, constructs the density descriptor with explicit physical dimension;Further, it is used as main descriptor, and the correlation model of glass component-density is constructed by adopting multiple descriptor optimal subset combination regression;For each oxide, introduce component concentration polynomial correction coefficient and key oxide interaction coefficient, characterize the non-additive of density contribution;And the model parameters are solved by using physical information constrained block alternation optimization algorithm.The application can complete density prediction by only using easily obtained basic parameters and a small amount of data, without a large amount of glass component-density data, without molecular dynamics simulation, the calculation efficiency is improved by more than 100 times, and without high-performance computing resources, significantly reduce the time cost and technical threshold of high-performance glass fiber research and development.

Description

Technical Field

[0001] This invention belongs to the field of glass fiber technology, and in particular to a method and system for predicting glass density based on dimensional constraint sign regression. Background Technology

[0002] Glass fiber density is one of the core physical quantities characterizing its structure and properties. Density not only directly determines the specific modulus and specific strength of the material, serving as a core indicator for measuring the lightweight level of glass fibers, but it is also closely related to elastic modulus, thermal expansion properties, dielectric properties, and melting and molding processes. It can indirectly reflect the atomic packing density and microstructure of the glass network. In fields with stringent requirements for weight reduction and high specific performance, such as aerospace, wind turbine blades, and high-end electronic substrates, the ability to quickly and accurately predict glass density during the formulation development stage often directly determines the R&D cycle, testing costs, and success rate of new glass fiber systems. Relying solely on experimental melting and calibration requires repeated batching, melting, molding, and density measurement processes, resulting in long cycles, high costs, and difficulty in efficiently screening target formulations in a high-dimensional, multi-component space. Therefore, developing a method to accurately calculate the density of glass fibers using only their components is of significant engineering importance for accelerating the development of high-performance glass fibers.

[0003] Currently, methods for calculating glass density from its components can be broadly classified into three categories, each with significant shortcomings. The first category is the classical additive method, such as the density addition equation proposed by Huggins and Stevens in their paper published in the Journal of the American Ceramic Society (HUGGINS, ML and STEVELS, JM (1954), Comparison of Two Equations for Calculation of Densities of Glasses from Their Compositions[J]. Journal of the American Ceramic Society, 37: 474-479.). This method calculates glass density by linearly adding each oxide with a fixed partial molar volume or density factor. This approach has also been adopted by numerous patent documents; however, the prediction error of this method increases significantly in mixed systems such as multi-component or high-density systems. The second category is empirical statistical regression, such as the polynomial global model built by Fluegel in his paper (Fluegel, A. Global Model for Calculating Room-Temperature Glass Density from the Composition[J]. Journal of the American Ceramic Society, 2007, 90: 2622-2625.) based on a large database of 6719 glass components, with a standard error of approximately 0.019 g / cm³. This type of method has a large number of fitting coefficients, weak physical meaning, and limited extrapolation ability for new systems with insufficient database coverage and for specific component ranges. The third category is machine learning, such as Deng's paper (Binghui Deng, Machine learning on density and elastic property of oxide glasses driven by large dataset[J], Journal of Non-Crystalline Solids, 2020). Density prediction models (Volume 529, 119768) trained on large-scale datasets have prediction accuracy that is highly dependent on the scale and quality of the training data. These models are "black box" characteristics, lack physical interpretability, and their prediction accuracy drops significantly outside the scope of the training data. In addition, while molecular dynamics simulations are physically rigorous, they are computationally intensive and rely on high-performance computing resources, making them difficult to meet the practical needs of rapid formulation screening.

[0004] In summary, existing methods for calculating glass density struggle to balance prediction accuracy, physical interpretability, and computational efficiency. This is especially true in multi-component high-density glass fiber systems, where large prediction errors and insufficient generalization are common defects. There is an urgent need for a glass fiber density prediction method that combines high accuracy, clear physical meaning, and high computational efficiency. Summary of the Invention

[0005] The purpose of this invention is to address the problems existing in the prior art by providing a glass density prediction method based on dimensionally constrained symbolic regression. This method uses dimensionally constrained symbolic regression to construct a density descriptor that accurately characterizes the relationship between fundamental physical quantities and glass density. Using this as the primary descriptor, a correlation model is established through optimal subset combination regression of multiple descriptors. Furthermore, polynomial correction coefficients varying with component concentration are introduced for each oxide, and interaction correction coefficients are introduced for key oxide pairs to characterize the non-additive nature of the glass density contribution. This method accurately predicts the density of multi-component glass systems without requiring extensive glass-component data or molecular dynamics simulations, significantly improving computational efficiency and providing theoretical guidance and technical support for the formulation design of high-performance glass fibers.

[0006] The technical solution to achieve the objective of this invention is as follows: On the one hand, a glass density prediction method based on dimensionally constrained sign regression is provided, the method comprising the following steps:

[0007] Step 1: Collect composition data and corresponding density experimental data of glass fibers in different systems to construct a dataset;

[0008] Step 2: Based on the dimensional constraint symbolic regression algorithm, key physical parameters are selected from multiple candidate physical parameters, and the main physical descriptor of glass density is constructed by combining the physical characteristics of each component unit in the glass fiber composition. Then, a correlation model between the main physical descriptor and the predicted glass density is established.

[0009] Step 3: Introduce a component concentration correction coefficient to characterize the nonlinear contribution of a single component and an interaction correction coefficient to characterize the coupling effect between different components into the master physical descriptor to obtain the corrected physical descriptor, and update the association model based on the corrected physical descriptor.

[0010] Step 4: Based on the dataset, the parameters in the correlation model are solved and optimized using an optimization algorithm that incorporates physical information constraints, thereby obtaining the trained glass density prediction model.

[0011] Step 5: Input the composition data of the glass to be predicted into the trained glass density prediction model, and output the corresponding glass density prediction result.

[0012] Furthermore, in step 2, the master physical descriptor is constructed using dimensionally constrained symbolic regression. The specific process includes:

[0013] Step 2-1: Assign corresponding physical dimension vectors to the candidate physical parameters, and use the dimension vector of glass density as the target root node dimension of the symbolic regression expression.

[0014] Step 2-2: In the process of symbolic regression evolution derivation, the dimensional type inference and dimensional compatibility verification are performed from bottom to top. Only the dimensionally compatible expressions are retained, and the search space is constrained to the subspace with legal dimensions.

[0015] Steps 2-3: Within the dimensionally valid subspace, search using an objective function that includes fitting error, expression complexity, and a dimensional consistency penalty term to obtain a set of expression solutions that balances accuracy and complexity.

[0016] Steps 2-4 involve resampling the samples and counting the selection frequency of each candidate physical parameter in the solution set of the high-precision, low-complexity expression. Low-frequency parameters with frequencies below a preset threshold are removed, and the simplest master physical descriptor that retains the key physical parameters is obtained by convergence. The threshold for high precision and low complexity is set by the user.

[0017] Furthermore, the candidate physical parameters include at least a variety of the following: molecular density, bond dissociation energy of cations, molar volume, network connectivity, average coordination number, electric field strength, relative molecular mass, dielectric constant, single bond strength, and melting point; the key physical parameters selected include at least molecular density and relative molecular mass; the master physical descriptor is obtained by combining the densities and relative molecular masses of each component oxide through a function, weighted and summed according to the molar ratio of the components, and normalized to the total number of atoms per mole.

[0018] Furthermore, the process of establishing the association model in step 2 specifically includes:

[0019] Steps 2-5: Based on the main physical descriptor, a candidate descriptor pool is automatically generated by applying a set of operators to the main physical descriptor and combining the component statistical features.

[0020] Steps 2-6: Use the sparse selection algorithm to select the subset of descriptors that minimizes the fitting error from the candidate descriptor pool, and ensure that the main physical descriptor is retained in this subset;

[0021] Steps 2-7 involve using an optimization algorithm to jointly optimize the combination coefficients of each descriptor in the descriptor subset, and constructing a multi-descriptor optimal subset combination regression model.

[0022] Furthermore, the component concentration correction coefficient in step 3 is a polynomial function that varies with the concentration of the corresponding component; the interaction correction coefficient is set on a preset set of key component pairs.

[0023] Furthermore, the solution and optimization process described in step 4 employs a block-based alternating optimization method with physical information constraints. The specific process includes:

[0024] Step 4-1: Construct a physical information composite loss function. The composite loss function is based on the mean square error between the predicted density and the experimental density, and is superimposed with a group sparse regularization term for controlling the adaptive correction polynomial order, an interaction sparse regularization term for eliminating insignificant component pairs, a dilution limit anchoring term for constraining the limiting behavior of components, and a physical boundary penalty term reflecting the chemical properties of the material structure. Among them, the dilution limit anchoring term means that when the concentration of a certain component tends to the preset dilution limit, the correction coefficient of the component concentration is anchored to 1.

[0025] Step 4-2: Decouple the trainable parameters of the associated model into a block of linear coefficients and a block of nonlinear correction coefficients;

[0026] Step 4-3: In iterative optimization, one set of parameters is fixed alternately while the other set of parameters is solved in a closed loop or iteratively updated based on gradients until the model converges.

[0027] Furthermore, the physical boundary penalty term is established based on the structural classification effect of each component in the glass fiber network, and the boundary violation amount that violates the known monotonicity change trend or exceeds the preset curvature threshold is penalized through the hinge function.

[0028] Furthermore, step 4 introduces a course-based training strategy based on density intervals: the training samples are divided into several density intervals according to the experimental density. The model is first trained in the medium-density interval with the largest sample size to fit the main trend, and then samples from extreme intervals such as low-density intervals or high-density intervals are gradually included for fine-tuning and optimization. The low-density interval, medium-density interval, and high-density interval are divided according to a custom threshold.

[0029] On the other hand, a glass density prediction system based on dimensionally constrained sign regression is provided for implementing the glass density prediction method based on dimensionally constrained sign regression. The system includes:

[0030] The first module is used to: collect composition data and corresponding density experimental data of glass fibers in different systems, and construct a dataset;

[0031] The second module is used to implement: a dimensional constraint-based symbolic regression algorithm to screen key physical parameters from multiple candidate physical parameters, and to construct a master physical descriptor of glass density by combining the physical characteristics of each component unit in the glass fiber composition, and then establish a correlation model between the master physical descriptor and the predicted glass density.

[0032] The third module is used to: introduce a component concentration correction coefficient to the main physical descriptor to characterize the nonlinear contribution of a single component, and an interaction correction coefficient to characterize the coupling effect between different components, to obtain a corrected physical descriptor, and update the association model based on the corrected physical descriptor;

[0033] The fourth module is used to: solve and optimize the parameters in the correlation model based on the dataset using an optimization algorithm that incorporates physical information constraints, thereby obtaining the trained glass density prediction model;

[0034] The fifth module is used to: input the composition data of the glass to be predicted into the trained glass density prediction model, and output the corresponding glass density prediction result.

[0035] On the other hand, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the glass density prediction method based on dimensional constraint symbolic regression.

[0036] Compared with the prior art, the significant advantages of this invention are:

[0037] (1) Symbolic regression based on dimensional constraints can automatically select the simplest descriptors with clear physical dimensions and clear physical meaning, which can avoid the defect of pure machine learning "black box" models whose prediction accuracy drops significantly outside the training data space.

[0038] (2) By introducing the polynomial correction coefficient of oxide concentration and the interaction coefficient of key oxide pairs, this invention can accurately characterize the nonlinear contribution of single oxide and the pairwise coupling contribution, and significantly reduce the density prediction error of multi-element glass with more than 8 elements.

[0039] (3) Density prediction can be completed using only readily available basic physical parameters and a small amount of experimental data. It does not require a large amount of component data or high-performance molecular dynamics simulation, thus improving computational efficiency by more than 100 times. It also does not require high-performance computing resources, significantly reducing the time cost and technical threshold for the development of high-performance glass.

[0040] (4) By integrating prior knowledge of glass structure chemistry, a composite loss function containing structured sparsity and physical boundary penalty was constructed. Combined with block-based alternating optimization and course-based training methods, the overfitting problem can be effectively suppressed, ensuring the extrapolation performance of the model in different density ranges and across systems.

[0041] (5) The multi-descriptor optimal subset combination regression modeling method proposed in this invention abandons the single-descriptor linear fitting approach. It automatically constructs a descriptor pool using the simplest physical descriptor F as the main descriptor. Through optimal subset sparse selection (main descriptor is constantly retained) and coefficient evolution optimization, the correlation model is established, upgrading the single linear mapping to a combination modeling method of "descriptor construction + optimal subset selection + coefficient evolution". It can more fully characterize the nonlinear correlation between glass fiber composition and density while maintaining the physical meaning of F.

[0042] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0043] Figure 1 This is a flowchart of a glass density prediction method based on dimensional constraint sign regression in one embodiment.

[0044] Figure 2 This is a schematic diagram illustrating the glass density prediction method generated by the present invention and the verification results for glass data of different systems in one embodiment.

[0045] Figure 3 This is a schematic diagram illustrating the verification results of predicting glass data of different systems based on a machine learning method (random forest model) in one embodiment. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0047] It should be noted that if the embodiments of the present invention involve descriptions such as "first" and "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" and "second" may explicitly or implicitly include at least one of those features. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0048] In one embodiment, a glass density prediction method based on dimensionally constrained sign regression is proposed, the method comprising the following steps:

[0049] Step 1: Collect composition data and corresponding density experimental data of glass fibers in different systems to construct a dataset;

[0050] Step 2: Based on the dimensional constraint symbolic regression algorithm, key physical parameters are selected from multiple candidate physical parameters, and the main physical descriptor of glass density is constructed by combining the physical characteristics of each component unit in the glass fiber composition. Then, a correlation model between the main physical descriptor and the predicted glass density is established.

[0051] Step 3: Introduce a component concentration correction coefficient to characterize the nonlinear contribution of a single component and an interaction correction coefficient to characterize the coupling effect between different components into the master physical descriptor to obtain the corrected physical descriptor, and update the association model based on the corrected physical descriptor.

[0052] Step 4: Based on the dataset, the parameters in the correlation model are solved and optimized using an optimization algorithm that incorporates physical information constraints, thereby obtaining the trained glass density prediction model.

[0053] Step 5: Input the composition data of the glass to be predicted into the trained glass density prediction model, and output the corresponding glass density prediction result.

[0054] Furthermore, in one embodiment, step 2 utilizes dimensional constraint-based symbolic regression to construct the master physical descriptor, specifically including:

[0055] Step 2-1: Assign corresponding physical dimension vectors to the candidate physical parameters, and use the dimension vector of glass density as the target root node dimension of the symbolic regression expression.

[0056] Step 2-2: In the process of symbolic regression evolution derivation, the dimensional type inference and dimensional compatibility verification are performed from bottom to top. Only the dimensionally compatible expressions are retained, and the search space is constrained to the subspace with legal dimensions.

[0057] Steps 2-3: Within the dimensionally valid subspace, search using an objective function that includes fitting error, expression complexity, and a dimensional consistency penalty term to obtain a set of expression solutions that balances accuracy and complexity.

[0058] Steps 2-4 involve resampling the samples and counting the selection frequency of each candidate physical parameter in the solution set of the high-precision, low-complexity expression. Low-frequency parameters with frequencies below a preset threshold are removed, and the simplest master physical descriptor that retains the key physical parameters is obtained by convergence. The threshold for high precision and low complexity is set by the user.

[0059] Preferably, in some embodiments, the candidate physical parameters include at least a plurality of the following: molecular density, bond dissociation energy of cations, molar volume, network connectivity, average coordination number, electric field strength, relative molecular mass, dielectric constant, single bond strength, and melting point; the key physical parameters selected include at least molecular density and relative molecular mass; the master physical descriptor is obtained by combining the densities and relative molecular masses of each component oxide by a function, weighted and summed according to the molar ratio of the components, and normalized to the total number of atoms per mole.

[0060] Furthermore, in one embodiment, the process of establishing the association model in step 2 specifically includes:

[0061] Steps 2-5: Based on the main physical descriptor, a candidate descriptor pool is automatically generated by applying a set of operators to the main physical descriptor and combining the component statistical features.

[0062] Steps 2-6: Use the sparse selection algorithm to select the subset of descriptors that minimizes the fitting error from the candidate descriptor pool, and ensure that the main physical descriptor is retained in this subset;

[0063] Steps 2-7 involve using an optimization algorithm to jointly optimize the combination coefficients of each descriptor in the descriptor subset, and constructing a multi-descriptor optimal subset combination regression model.

[0064] Furthermore, in one embodiment, the component concentration correction coefficient in step 3 is a polynomial function that varies with the concentration of the corresponding component; the interaction correction coefficient is set on a preset set of key component pairs.

[0065] Furthermore, in one embodiment, the solution and optimization process in step 4 employs a block-based alternating optimization method with physical information constraints, specifically including:

[0066] Step 4-1: Construct a physical information composite loss function. The composite loss function is based on the mean square error between the predicted density and the experimental density, and is superimposed with a group sparse regularization term for controlling the adaptive correction polynomial order, an interaction sparse regularization term for eliminating insignificant component pairs, a dilution limit anchoring term for constraining the limiting behavior of components, and a physical boundary penalty term reflecting the chemical properties of the material structure. Among them, the dilution limit anchoring term means that when the concentration of a certain component tends to the preset dilution limit, the correction coefficient of the component concentration is anchored to 1.

[0067] Step 4-2: Decouple the trainable parameters of the associated model into a block of linear coefficients and a block of nonlinear correction coefficients;

[0068] Step 4-3: In iterative optimization, one set of parameters is fixed alternately while the other set of parameters is solved in a closed loop or iteratively updated based on gradients until the model converges.

[0069] Preferably, in some embodiments, the physical boundary penalty term is established based on the structural classification effect of each component in the glass fiber network, and a penalty is imposed on the out-of-bounds amount that violates the known monotonicity trend or exceeds the preset curvature threshold through the hinge function.

[0070] Furthermore, in one embodiment, step 4 introduces a course-based training strategy divided by density intervals: the training samples are divided into several density intervals according to the experimental density. The model is first trained in the medium-density interval with the largest sample size to fit the main trend, and then samples from extreme intervals such as low-density or high-density intervals are gradually included for fine-tuning and optimization. The low-density interval, medium-density interval, and high-density interval are divided according to a custom threshold.

[0071] Compared to the traditional partial molar volume summation method, this invention significantly reduces the prediction error for multi-component glasses (8 or more components). Simultaneously, it retains the clear physical meaning based on oxide density and relative molecular mass, avoiding the problem of significantly reduced prediction accuracy outside the training data space encountered by pure machine learning methods. Furthermore, this invention can complete density prediction using only readily available basic parameters such as oxide density, relative molecular mass, and molar number of atoms, along with a small amount of data. It eliminates the need for extensive glass composition-density data and molecular dynamics simulations, improving computational efficiency by more than a hundredfold. Moreover, it requires no high-performance computing resources, significantly reducing the time cost and technical barriers to high-performance glass fiber development.

[0072] Specifically, preferably, in one embodiment, combined with Figure 1 A method for predicting glass density based on dimensionally constrained sign regression is proposed, the method comprising:

[0073] Step 1: Collect composition data and corresponding density data of glass fibers from different systems to construct a dataset;

[0074] Step 2: Based on the dimensional constraint symbolic regression method, key physical parameters are screened from multiple candidate physical parameters, and the density descriptor F of glass fiber is constructed by combining the physical characteristics of each oxide in the glass composition, and a correlation model between the density descriptor F and the glass density is established.

[0075] Step 3: Introduce polynomial correction coefficients that vary with the concentration of each oxide component and interaction correction coefficients that characterize the coupling between key oxide pairs to the density descriptor F, thereby obtaining the corrected descriptor, and update the association model based on the corrected descriptor.

[0076] Step 4: Based on the dataset, construct a composite loss function that includes structured sparsity constraints and physical consistency constraints, and use a block-based alternating optimization algorithm to solve and optimize the parameters in the updated association model to obtain the optimized glass density prediction model.

[0077] Step 5: For the glass to be predicted, input its composition data into the optimized glass density prediction model and output the corresponding glass density prediction result.

[0078] Preferably, in some embodiments, step 2, the process of constructing the density descriptor F using dimensional constraint-based symbolic regression, includes:

[0079] Step 2-1: Assign a corresponding physical dimension vector to each parameter in the candidate physical parameter set, and use the dimension vector of glass density as the target dimension of the root node of the symbolic regression expression tree.

[0080] Preferably, the set of candidate physical parameters includes molecular density, bond dissociation energy of cations, molar volume, network connectivity, average coordination number, electric field strength, relative molecular mass, dielectric constant, single bond strength, and melting point parameter; wherein dimensionless quantities such as network connectivity, average coordination number, and relative molecular mass are assigned zero vectors, and molecular density is assigned density dimensions.

[0081] Step 2-2: Represent the candidate descriptors as an expression tree. During the generation and evolution of the expression tree, perform dimensional type inference from the bottom up, retain only dimensionally compatible expressions, and shrink the expression search space to a dimensionally valid subspace. ;

[0082] Preferably, the set of operators includes addition, subtraction, multiplication, division, square root, and square; during population initialization, subtree crossover, and subtree mutation, the dimension type of the expression tree is inferred from bottom to top—addition and subtraction operators require that the dimension vectors of the two child nodes are equal, multiplication and division operators add or subtract the dimension vectors of the two child nodes component by component, square root operators require that each dimension component is even and halve it, square operators double each component, and exponential, logarithmic, and trigonometric operators require that the independent variable is dimensionless;

[0083] Steps 2-3: Within the dimensionally valid subspace, perform an evolutionary search with an objective function that includes fitting error, expression complexity, and a dimensional consistency penalty term, and output a set of Pareto front expressions that balance accuracy and complexity.

[0084] Here, the objective function Represented as:

[0085]

[0086] In the formula, Let j be the physical parameter vector of the j-th sample. For the corresponding experimental density, The expression complexity is denoted by α, where α is the complexity penalty coefficient. As a dimensional consistency penalty term, it is the sum of the norms of the differences between the dimensional vectors on both sides of each addition and subtraction node. This represents the weighting coefficient of the penalty term. Wherein, the fitting target... This contributes to the density of the single oxides obtained by decomposition according to the component molar ratio.

[0087] Steps 2-4 involve self-resampled samples and the frequency of each candidate physical parameter in the high-precision, low-complexity Pareto front expression is counted. Low-frequency parameters are removed according to the preset selection frequency threshold, and the simplest density descriptor that retains the key physical parameters is obtained by convergence.

[0088] Here, the key physical parameters selected are molecular density and relative molecular mass;

[0089] Here, the density descriptor is specifically represented as: the product of the square root of the density of each oxide and its relative molecular mass, weighted and summed according to the molar ratio of the components, and normalized to the total number of molar atoms per unit glass, as shown in the formula:

[0090]

[0091] In the formula, For density descriptor, Let represent the total number of atoms in the model, i represent the number of oxide types, and oxide represent the total number of oxide types. Let i be the molar ratio of the components of the i-th oxide. Let be the relative molecular mass of the i-th oxide. Let be the density of the i-th oxide.

[0092] The specific analysis is as follows: Under the constraint of the target dimension of glass density, the product of the square root of molecular density ρ and the dimensionless relative molecular mass M can satisfy the target dimension of density with the lowest complexity and is stably retained because its selection frequency is significantly higher than the threshold. The other eight parameters either introduce dimensions incompatible with density or do not contribute to dimensional balancing and are systematically eliminated. Thus, the convergence yields only the two key parameters of molecular density ρ and relative molecular mass M, and the form is the simplest expression of the product of the square root of the density of each oxide and its relative molecular mass.

[0093] Preferably, in some embodiments, the process of establishing the association model in step 2 includes:

[0094] Steps 2-5 involve using the density descriptor F as the primary descriptor and F as the basis. By applying a set of operators to F through symbolic regression and combining them with component statistical features, a set of candidate descriptors Φ1, Φ2, …, Φm is automatically generated, forming a descriptor pool {Φ1, …, Φm}. m Furthermore, the generation process does not alter the functional form of the main descriptor F;

[0095] Steps 2-6, with the root mean square error of the fit as the objective, and under the constraint of the upper limit of the number of descriptors, employ... Optimal subset regression searches the candidate descriptor pool for the subset of descriptors that minimizes the root mean square error of the fit. And ensure that the main descriptor F is always retained in the descriptor subset Ω;

[0096] Steps 2-7 involve using an evolutionary algorithm to jointly optimize the combination coefficients of each descriptor in the descriptor subset, resulting in a multi-descriptor combination regression model of density descriptor and glass density, i.e., the optimal subset combination regression model of multiple descriptors, which serves as the correlation model.

[0097]

[0098] In the formula, To predict density, For the descriptor subset Ω, the first One descriptor, , The coefficients are obtained through fitting and evolutionary optimization, and D is the upper limit of the number of descriptors.

[0099] Preferably, in some embodiments, step 3 applies polynomial correction coefficients and interaction correction coefficients to the main descriptor F to obtain the corrected descriptor F':

[0100]

[0101] In the formula, For the corrected descriptor, The total number of atoms in the model is represented by i, and the numbers i and j represent the types of oxides. , The molar ratios of the components of the i-th and j-th oxides are respectively. , Let be the density and relative molecular mass of the i-th oxide, respectively. , Here, represents the density and relative molecular mass of the j-th oxide, respectively. Let be the polynomial correction coefficient for the i-th oxide as a function of component concentration. Let P be the set of key oxide pairs with physical mechanisms, and let P be the interaction correction coefficient between oxides i and j. Furthermore, for oxides with anomalous coordination numbers, the range of values ​​for the second-order curvature coefficient in their polynomial correction coefficients is broadened, and the interaction correction coefficient between them and the modifying oxides is enabled. .

[0102] Here, the oxides are classified into three categories according to their role in the glass network: network-forming bodies, intermediate bodies, and modifiers. Different initial value ranges and constraints are set for the polynomial correction coefficients and interaction coefficients of different categories. For oxides with coordination number anomalous (including B2O3 and Al2O3), their second-order curvature coefficients are relaxed. The range of values ​​for and its interaction coefficient with the modified oxide. It is enabled to characterize non-monotonic contributions such as boron anomalies and aluminum anomalies.

[0103] Preferably, the second-order curvature coefficients of B2O3 and Al2O3 with coordination number anomalous are considered. The value range is broadened to [-0.10, 0.10].

[0104] Preferably, in some embodiments, the composite loss function in step 4 includes: based on the root mean square error between the predicted density and the experimental density, superimposed a group sparse regularization term for controlling the adaptive correction polynomial order, an interaction sparse regularization term for eliminating insignificant oxide pairs, a dilution limit anchoring term to constrain the zero-order correction coefficient of oxides to approach 1, and a physical boundary penalty term reflecting structural chemical properties, expressed as:

[0105]

[0106] In the formula, L is the composite loss function, and n is the number of training samples. , Let be the predicted density and the corresponding experimental density measurement value of the j-th sample, respectively. Here, K is the regularization coefficient, and K is the polynomial order. For each oxide's higher-order coefficients { , …, The applied group sparsity regularization coefficients compress unnecessary higher-order terms to zero as a whole, thereby achieving adaptive determination of the order of each oxide modified polynomial. For the i-th oxide, the k-th order coefficients are used. Interaction correction coefficient The sparsity regularization coefficient allows insignificant oxide pairs to be automatically eliminated. The dilution limit anchoring coefficients constrain the zero-order correction coefficients for each oxide. The value approaches 1 to ensure that the density contribution returns to its intrinsic value when the oxide content approaches zero; P is the set of key oxide pairs with the physical mechanism. Its weighting coefficient, This is a physical boundary penalty term.

[0107] Preferably, the zeroth-order correction coefficient The initial value range is set to [0.5, 2.0], and the higher-order coefficients are... The initial range of values ​​for (k≥1) is set to [-0.05, 0.05], and the initial value of the polynomial order K is 2.

[0108] Preferably, here, , , , , The value range is set to [1×10]. -6 1×10 -2 ].

[0109] Preferably, in some embodiments, the physical boundary penalty term It consists of two parts: monotonicity out-of-bounds penalty and curvature out-of-bounds penalty. The out-of-bounds quantities are summed after squaring the values ​​using a hinge function. The expression is:

[0110]

[0111] In the formula, , The correction coefficient polynomials for the i-th oxide are respectively Its component concentration The first and second derivatives; The desired monotonic direction of the i-th oxide is indicated by +1 or -1 based on the known density-composition variation trend of the oxide as a network or modified body (when...). · >0 means that the correction coefficient is positive when its direction of change with concentration deviates from the known trend; otherwise, it is zero. The maximum allowable curvature threshold for the i-th oxide is determined by taking a larger value for B2O3 and Al2O3, which have coordination number anomalous. To allow for its non-monotonic contribution, smaller values ​​are taken for the remaining oxides. ; This is a hinge function that only penalizes out-of-bounds portions.

[0112] Preferably, in some embodiments, the block-alternating optimization algorithm in step 4 specifically includes:

[0113] The trainable parameters of the association model are decoupled into descriptor combination coefficient blocks consisting of linear coefficients. and a block of nonlinear correction coefficients composed of nonlinear parameters. ;

[0114] In each iteration:

[0115] (a) Fix the current nonlinear correction coefficient block, forward compute the descriptor values ​​of all samples on the descriptor subset Ω, and directly solve the descriptor combination coefficient block using the least squares closed-form solution (since the prediction density affects the descriptor combination coefficients). (for linear)

[0116] (b) Fix the current descriptor combination coefficient block, use backpropagation (automatic differentiation) to calculate the gradient of the composite loss function with respect to the nonlinear correction coefficient block, and use the adaptive moment estimation (Adam) optimizer to... The nonlinear correction coefficient block is updated accordingly.

[0117] (c) Alternately execute (a) and (b) above until the convergence condition is met.

[0118] The update formula for the Adam optimizer is as follows:

[0119]

[0120] In the formula, , These are the nonlinear correction coefficient blocks for the t-th and (t-1)-th iterations, respectively. Let be the gradient of the loss function with respect to the parameters in the t-th iteration. , Let be the first moment and the second moment estimates for the t-th iteration, respectively, and η be the learning rate. , These are the first-order moment attenuation coefficient and the second-order moment attenuation coefficient, respectively. For numerically stable terms, , These are the first-order moment estimates and second-order moment estimates after bias correction, respectively; The gradient operator for taking the partial derivative with respect to the nonlinear correction coefficient block θ. Let be the composite loss function.

[0121] Preferably, the learning rate η is 0.01, and the first-order moment decay coefficient is... The value is 0.9, which is the second-order moment attenuation coefficient. The value is 0.999, a numerically stable term. The value is 1×10 -8 The number of samples in a small batch is 32.

[0122] Preferably, in some embodiments, step 4 further employs a course-based training strategy based on density intervals during the optimization process: the training samples are divided into multiple density intervals according to the experimental density, and the main trend of the model is trained first in the medium-density interval with the largest sample size, and then samples from the low-density interval and high-density interval are gradually included for fine-tuning training; during the training process, the system-retaining cross-validation (i.e., cross-validation is divided according to the glass system rather than random samples, and a complete system is reserved for validation each time) is used to select the polynomial order and regularization coefficients, and the loss on the validation set is used as the early stopping criterion.

[0123] Specifically, the order of the polynomial K and the regularization coefficients are selected by using a system-based cross-validation (i.e., dividing the cross-validation fold according to the glass system rather than random samples, reserving a complete system for validation each time). , , , , Training will stop when any of the following conditions are met:

[0124] ① The number of training epochs exceeds the first preset threshold;

[0125] ② The improvement in the loss of the consecutive U-round validation set is less than the second preset threshold;

[0126] ③RMSE < third preset threshold;

[0127] The units for the second and third preset thresholds are both g / cm³.

[0128] Preferably, the first preset threshold is 500, the second preset threshold is 0.001 g / cm³, and the third preset threshold is 0.01 g / cm³. 3 .

[0129] Preferably, in some embodiments, the method further includes performing the following after step 4:

[0130] Based on the dataset, data from different density ranges were used to validate the generalization ability of the association model, and adjustments were made according to the validation results to obtain the final association model; specifically including:

[0131] Using the optimized glass density prediction model from step 4, density prediction is performed on the validation set data outside the training set, and the prediction error of the validation set is calculated. If the prediction error of the validation set is greater than the error of the training set and the difference exceeds a preset threshold, the polynomial order K is reduced and the L2 regularization coefficient is increased. Increase the group sparsity regularization coefficient Increase the sparsity regularization coefficient of the interaction. Adjust hyperparameters such as the learning rate or expand the training set, and then return to step 4 to re-optimize the association model.

[0132] In summary, the method proposed in this invention has the following characteristics: (1) The dimension-constrained symbolic regression descriptor for glass fiber density in this invention assigns dimension vectors to the physical parameters of ten glass oxides in symbolic regression, performs dimension type inference with the glass density dimension as the target dimension, shrinks the search space to a dimensionally valid subspace and superimposes a dimension consistency penalty. Compared with the pure data-driven general symbolic regression, this method converges faster and naturally converges under dimension constraints to obtain the simplest physical descriptor F, which is composed only of molecular density and relative molecular mass and has homogeneous dimensions, thus ensuring physical interpretability from an algorithmic perspective. (2) The multi-descriptor optimal subset combination regression modeling method proposed in this invention abandons single-descriptor linear fitting, automatically constructs a descriptor pool with F as the main descriptor, and establishes an association model through optimal subset sparse selection (main descriptor is always retained) and coefficient evolution optimization, upgrading the single linear mapping to a combination modeling of "descriptor construction + optimal subset selection + coefficient evolution", which more fully characterizes the nonlinear relationship between glass fiber composition and density while maintaining the physical meaning of F. (3) The glass oxide concentration-dependent non-additive modeling method proposed in this invention introduces a polynomial correction coefficient that varies with concentration for each oxide. , introduces interaction correction coefficients for key oxide pairs Based on this, F is corrected to obtain F'. Compared with constant or single-variable correction, it can simultaneously characterize the nonlinear contribution of single oxide and the pairwise coupling contribution, significantly reducing the density prediction error of multivariate system. (4) The proposed method of physical information constraint block alternating optimization based on the prior chemical knowledge of glass structure can construct a composite loss function containing group sparsity (order adaptive), interaction sparsity, sparse limit anchoring and physical boundary penalty; decouple the parameters into combination coefficient blocks and correction coefficient blocks for alternating iteration, solving the convergence problem of linear-nonlinear mixture; and with the group initialization of network body / intermediate body / modification body, course-based training and system-based cross-validation, it can achieve the purpose of suppressing overfitting and ensuring generalization compared with pure machine learning and simple fitting.

[0133] In one embodiment, a glass density prediction system based on dimensionally constrained sign regression is provided for implementing the glass density prediction method based on dimensionally constrained sign regression. The system includes:

[0134] The first module is used to: collect composition data and corresponding density experimental data of glass fibers in different systems, and construct a dataset;

[0135] The second module is used to implement: a dimensional constraint-based symbolic regression algorithm to screen key physical parameters from multiple candidate physical parameters, and to construct a master physical descriptor of glass density by combining the physical characteristics of each component unit in the glass fiber composition, and then establish a correlation model between the master physical descriptor and the predicted glass density.

[0136] The third module is used to: introduce a component concentration correction coefficient to the main physical descriptor to characterize the nonlinear contribution of a single component, and an interaction correction coefficient to characterize the coupling effect between different components, to obtain a corrected physical descriptor, and update the association model based on the corrected physical descriptor;

[0137] The fourth module is used to: solve and optimize the parameters in the correlation model based on the dataset using an optimization algorithm that incorporates physical information constraints, thereby obtaining the trained glass density prediction model;

[0138] The fifth module is used to: input the composition data of the glass to be predicted into the trained glass density prediction model, and output the corresponding glass density prediction result.

[0139] Specific limitations regarding the glass density prediction system based on dimensionally constrained symbolic regression can be found in the limitations of the glass density prediction method based on dimensionally constrained symbolic regression mentioned above, and will not be repeated here. Each module in the aforementioned glass density prediction system based on dimensionally constrained symbolic regression can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0140] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements:

[0141] Step 1: Collect composition data and corresponding density experimental data of glass fibers in different systems to construct a dataset;

[0142] Step 2: Based on the dimensional constraint symbolic regression algorithm, key physical parameters are selected from multiple candidate physical parameters, and the main physical descriptor of glass density is constructed by combining the physical characteristics of each component unit in the glass fiber composition. Then, a correlation model between the main physical descriptor and the predicted glass density is established.

[0143] Step 3: Introduce a component concentration correction coefficient to characterize the nonlinear contribution of a single component and an interaction correction coefficient to characterize the coupling effect between different components into the master physical descriptor to obtain the corrected physical descriptor, and update the association model based on the corrected physical descriptor.

[0144] Step 4: Based on the dataset, the parameters in the correlation model are solved and optimized using an optimization algorithm that incorporates physical information constraints, thereby obtaining the trained glass density prediction model.

[0145] Step 5: Input the composition data of the glass to be predicted into the trained glass density prediction model, and output the corresponding glass density prediction result.

[0146] For specific limitations on each step, please refer to the limitations on the glass density prediction method based on dimensional constraint symbolic regression mentioned above, which will not be repeated here.

[0147] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being implemented when executed by a processor:

[0148] Step 1: Collect composition data and corresponding density experimental data of glass fibers in different systems to construct a dataset;

[0149] Step 2: Based on the dimensional constraint symbolic regression algorithm, key physical parameters are selected from multiple candidate physical parameters, and the main physical descriptor of glass density is constructed by combining the physical characteristics of each component unit in the glass fiber composition. Then, a correlation model between the main physical descriptor and the predicted glass density is established.

[0150] Step 3: Introduce a component concentration correction coefficient to characterize the nonlinear contribution of a single component and an interaction correction coefficient to characterize the coupling effect between different components into the master physical descriptor to obtain the corrected physical descriptor, and update the association model based on the corrected physical descriptor.

[0151] Step 4: Based on the dataset, the parameters in the correlation model are solved and optimized using an optimization algorithm that incorporates physical information constraints, thereby obtaining the trained glass density prediction model.

[0152] Step 5: Input the composition data of the glass to be predicted into the trained glass density prediction model, and output the corresponding glass density prediction result.

[0153] For specific limitations on each step, please refer to the limitations on the glass density prediction method based on dimensional constraint symbolic regression mentioned above, which will not be repeated here.

[0154] As a specific example, the invention will be further verified and illustrated in one embodiment.

[0155] This embodiment implements the glass density prediction method proposed in this invention, specifically including:

[0156] (1) Collect the composition and density data of multi-element glass materials, in which the oxides are the types required for conventional glass fibers, including SiO2, B2O3, Al2O3, MgO, CaO, Li2O, Na2O, K2O, Fe2O3, TiO2, ZrO2, ZnO, CeO2, Y2O3, La2O3 and SrO.

[0157] (2) Based on the glass composition in the collected data, calculate the total number of atoms per mole in each glass data, including cations and oxygen atoms of different oxides.

[0158] (3) Constructing a feature dataset: Ten candidate physical parameters are collected for each oxide as independent variable features x1~x 10 (Molecular density, bond dissociation energy of cations, molar volume, network connectivity, coordination number, electric field strength, molecular mass, dielectric constant, single bond strength, melting point), with the density contribution of each oxide according to the molar ratio of the components as the fitting target y. The 10 physical parameters corresponding to each oxide are shown in Table 1 below:

[0159] Table 1. Physical parameters of 10 different oxides

[0160]

[0161] (4) Constructing a glass density descriptor using dimensionally constrained symbolic regression: Assign dimensional vectors to each parameter and use the glass density dimension as the target dimension, in the dimensionally valid subspace Evolutionary search, filtering by inclusion frequency, converges to the simplest expression. The density descriptor is obtained by weighting the components according to their molar ratios and normalizing it to the total number of atoms per mole. .

[0162] (5) Using F as the primary descriptor, automatically construct the descriptor pool through symbolic regression (e.g., F, F). 2 , (etc.), under the constraint of an upper limit of the number of descriptors D=2, a subset Ω is selected by optimal subset regression (the main descriptor is always retained), and a multi-descriptor combined regression model is obtained through coefficient evolution optimization. As an example, the selected subset is Ω={F, F 2 The fitted correlation model is as follows:

[0163]

[0164] (6) First, apply polynomial correction coefficients and interaction correction coefficients to F to obtain F'. Then, replace F with F' and repeat the above combined regression. The polynomial correction coefficients of each oxide are obtained by block-based alternating optimization with physical information constraints, as shown in Table 2. At the same time, the interaction correction coefficients of different oxide pairs are obtained. As shown in Table 3, the remaining insignificant oxide pairs are compressed to zero after interaction sparsity regularization.

[0165] Table 2 Correction coefficients for polynomials of different oxides

[0166] <![CDATA[SiO2]]> 1.01 0.0008 -0.00002 <![CDATA[B2O3]]> 0.94 -0.0021 0.00004 <![CDATA[Al2O3]]> 1.08 0.0015 -0.00003 MgO 1.12 -0.0026 0.00006 CaO 1.05 -0.0012 0.00003 <![CDATA[Li2O]]> 0.88 0.0040 -0.00010 <![CDATA[Na2O]]> 0.96 0.0009 -0.00002 <![CDATA[K2O]]> 0.91 0.0018 -0.00004 <![CDATA[Fe2O3]]> 1.15 0.0030 -0.00007 <![CDATA[TiO2]]> 1.06 -0.0010 0.00003 <![CDATA[ZrO2]]> 1.22 0.0021 -0.00005 ZnO 1.10 0.0014 -0.00003 <![CDATA[CeO2]]> 1.18 0.0026 -0.00006 <![CDATA[Y2O3]]> 1.03 0.0011 -0.00002 <![CDATA[La2O3]]> 0.97 0.0017 -0.00004 SrO 1.09 -0.0008 0.00002

[0167] Table 3. Interaction correction coefficients for different oxide pairs

[0168]

[0169] (7) Verify the accuracy of the model using glass data from different systems. Figure 2 The verification results of the model proposed in this invention show that the predicted density of different glass systems is basically consistent with the experimentally tested density (R0). 2 =0.979). Figure 3 The results are based on machine learning methods (random forest model). It can be seen that the predicted density of some glass components is close to the experimental density, but there are still a few glass components outside the training data space whose predicted density differs significantly from the experimental density (R0). 2 =0.796).

[0170] (8) The generalizability of the model proposed in this invention was verified by glass experimental data. The glass composition and density are shown in Table 4 below. (Here, the verification was carried out by glass experimental sample data with different compositions. The glass experimental sample data used are recorded as Experiment 1, Experiment 2, Experiment 3, Experiment 4, Experiment 5 and Experiment 6 as shown in Table 4.)

[0171] Table 4 Glass composition and predicted and actual density

[0172]

[0173] As shown in Table 4, in different density ranges, the error between the glass density calculated based on the method proposed in this invention and the experimental density is less than ±0.01 g / cm³. 3This fully demonstrates that the fiber glass density prediction method proposed in this invention has good generalization ability and accurate prediction of fiber glass density, which is helpful for designing high-performance glass fiber compositions. However, the error in predicting glass density based on machine learning (random forest model) shows different results within different ranges. For Experiments 1-3, when the glass composition range is close to the training data, the accuracy of the glass density prediction based on the machine learning method is high, indicating that the machine learning method has good accuracy in predicting glass density within the training set range. However, the error is not negligible for glass density outside the training set range. For example, in Experiments 4, 5, and 6, the prediction error of glass density all exceeds 0.05 g / cm³. 3 The maximum value reached 0.162 g / cm³. 3 .

[0174] In summary, this invention can accurately predict the density of glass fibers in different systems, while simplifying the calculation process and improving calculation efficiency. It can effectively solve the problem of weak generalization of existing glass density prediction methods and provide an effective tool for the rapid design of high-performance glass fibers.

[0175] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.

Claims

1. A method for predicting glass density based on dimensionally constrained sign regression, characterized in that, The method includes the following steps: Step 1: Collect composition data and corresponding density experimental data of glass fibers in different systems to construct a dataset; Step 2: Based on the dimensional constraint symbolic regression algorithm, key physical parameters are selected from multiple candidate physical parameters, and the main physical descriptor of glass density is constructed by combining the physical characteristics of each component unit in the glass fiber composition. Then, a correlation model between the main physical descriptor and the predicted glass density is established. Step 3: Introduce a component concentration correction coefficient to characterize the nonlinear contribution of a single component and an interaction correction coefficient to characterize the coupling effect between different components into the master physical descriptor to obtain the corrected physical descriptor, and update the association model based on the corrected physical descriptor. Step 4: Based on the dataset, the parameters in the correlation model are solved and optimized using an optimization algorithm that incorporates physical information constraints, thereby obtaining the trained glass density prediction model. Step 5: Input the composition data of the glass to be predicted into the trained glass density prediction model, and output the corresponding glass density prediction result.

2. The glass density prediction method based on dimensionally constrained sign regression according to claim 1, characterized in that, Step 2 utilizes dimensional constraint-based symbolic regression to construct the master physical descriptor. The specific process includes: Step 2-1: Assign corresponding physical dimension vectors to the candidate physical parameters, and use the dimension vector of glass density as the target root node dimension of the symbolic regression expression. Step 2-2: In the process of symbolic regression evolution derivation, the dimensional type inference and dimensional compatibility verification are performed from bottom to top. Only the dimensionally compatible expressions are retained, and the search space is constrained to the subspace with legal dimensions. Steps 2-3: Within the dimensionally valid subspace, search using an objective function that includes fitting error, expression complexity, and a dimensional consistency penalty term to obtain a set of expression solutions that balances accuracy and complexity. Steps 2-4 involve resampling the samples and counting the selection frequency of each candidate physical parameter in the solution set of the high-precision, low-complexity expression. Low-frequency parameters with frequencies below a preset threshold are removed, and the simplest master physical descriptor that retains the key physical parameters is obtained by convergence. The threshold for high precision and low complexity is set by the user.

3. The glass density prediction method based on dimensionally constrained sign regression according to claim 2, characterized in that, The candidate physical parameters include at least a variety of the following: molecular density, bond dissociation energy of cations, molar volume, network connectivity, average coordination number, electric field strength, relative molecular mass, dielectric constant, single bond strength, and melting point; the key physical parameters selected include at least molecular density and relative molecular mass; the master physical descriptor is obtained by combining the densities and relative molecular masses of each component oxide through a function, weighting the sum according to the molar ratio of the components, and normalizing it to the total number of atoms per mole.

4. The glass density prediction method based on dimensionally constrained sign regression according to claim 3, characterized in that, The process of establishing the association model in step 2 specifically includes: Steps 2-5: Based on the main physical descriptor, a candidate descriptor pool is automatically generated by applying a set of operators to the main physical descriptor and combining the component statistical features. Steps 2-6: Use the sparse selection algorithm to select the subset of descriptors that minimizes the fitting error from the candidate descriptor pool, and ensure that the main physical descriptor is retained in this subset; Steps 2-7 involve using an optimization algorithm to jointly optimize the combination coefficients of each descriptor in the descriptor subset, and constructing a multi-descriptor optimal subset combination regression model.

5. The glass density prediction method based on dimensionally constrained sign regression according to claim 1, characterized in that, The component concentration correction coefficient mentioned in step 3 is a polynomial function that varies with the concentration of the corresponding component; the interaction correction coefficient is set on a preset set of key component pairs.

6. The glass density prediction method based on dimensionally constrained sign regression according to claim 5, characterized in that, The solution and optimization process described in step 4 employs a block-based alternating optimization method with physical information constraints. The specific process includes: Step 4-1: Construct a physical information composite loss function. The composite loss function is based on the mean square error between the predicted density and the experimental density, and is superimposed with a group sparse regularization term for controlling the adaptive correction polynomial order, an interaction sparse regularization term for eliminating insignificant component pairs, a dilution limit anchoring term for constraining the limiting behavior of components, and a physical boundary penalty term reflecting the chemical properties of the material structure. Among them, the dilution limit anchoring term means that when the concentration of a certain component tends to the preset dilution limit, the correction coefficient of the component concentration is anchored to 1. Step 4-2: Decouple the trainable parameters of the associated model into a block of linear coefficients and a block of nonlinear correction coefficients; Step 4-3: In iterative optimization, one set of parameters is fixed alternately while the other set of parameters is solved in a closed loop or iteratively updated based on gradients until the model converges.

7. The glass density prediction method based on dimensionally constrained sign regression according to claim 6, characterized in that, The physical boundary penalty term is established based on the structural classification effect of each component in the glass fiber network, and the boundary excess is penalized by the hinge function for violations of known monotonicity change trends or exceeding the preset curvature threshold.

8. The glass density prediction method based on dimensionally constrained sign regression according to claim 6, characterized in that, Step 4 also introduces a course-based training strategy based on density intervals: the training samples are divided into several density intervals according to the experimental density. The model is first trained in the medium-density interval with the largest sample size to fit the main trend, and then samples from extreme intervals such as low-density intervals or high-density intervals are gradually included for fine-tuning and optimization. The low-density interval, medium-density interval and high-density interval are divided according to a custom threshold.

9. A glass density prediction system based on dimensionally constrained sign regression, used to implement the method as described in any one of claims 1 to 8, characterized in that, The system includes: The first module is used to: collect composition data and corresponding density experimental data of glass fibers in different systems, and construct a dataset; The second module is used to implement: a dimensional constraint-based symbolic regression algorithm to screen key physical parameters from multiple candidate physical parameters, and to construct a master physical descriptor of glass density by combining the physical characteristics of each component unit in the glass fiber composition, and then establish a correlation model between the master physical descriptor and the predicted glass density. The third module is used to: introduce a component concentration correction coefficient to the main physical descriptor to characterize the nonlinear contribution of a single component, and an interaction correction coefficient to characterize the coupling effect between different components, to obtain a corrected physical descriptor, and update the association model based on the corrected physical descriptor; The fourth module is used to: solve and optimize the parameters in the correlation model based on the dataset using an optimization algorithm that incorporates physical information constraints, thereby obtaining the trained glass density prediction model; The fifth module is used to: input the composition data of the glass to be predicted into the trained glass density prediction model, and output the corresponding glass density prediction result.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 8.

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